where \(E\)  is the energy of the produced particle (charmed meson), \(x_F\) 
is the Feynman variable, \(\sigma _{pA}\)  is the inelastic proton-Air
cross section and
\(d\sigma /dx_F\)  is the differential cross section for the charmed meson
production. Following previous
studies [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]},
we will assume that \(A = 14\) , i.e. we will
take the \(^{14}N\)  nucleus as the most representative element in
the composition of the atmosphere.
For this value of the atomic mass number, it is a reasonable
approximation to assume that \(\sigma _{pA \rightarrow charm} \approx A \times \sigma _{pp \rightarrow charm}\) . Surely a more refine analysis
of these two aspects is possible but would shadow our discussion
of the selected issues. For \(\sigma _{pA}\)  we will assume the prediction
presented in Ref. [10]} (for a more detailed
discussion see Ref. [11]}).
